The Annals of Probability

Stochastic calculus for symmetric Markov processes

Z.-Q. Chen, P. J. Fitzsimmons, K. Kuwae, and T.-S. Zhang

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Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

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Ann. Probab., Volume 36, Number 3 (2008), 931-970.

First available in Project Euclid: 9 April 2008

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Zentralblatt MATH identifier

Primary: 31C25: Dirichlet spaces
Secondary: 60J57: Multiplicative functionals 60J55: Local time and additive functionals 60H05: Stochastic integrals

Symmetric Markov process time reversal stochastic integral generalized Itô formula additive functional martingale additive functional dual additive functional Revuz measure dual predictable projection


Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S. Stochastic calculus for symmetric Markov processes. Ann. Probab. 36 (2008), no. 3, 931--970. doi:10.1214/07-AOP347.

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